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https://link.springer.com/article/10.1007/JHEP09(2015)148
DOI: 10.1007/JHEP09(2015)148
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by Societa Italiana di Fisica. All rights reserved.
JHEP09(2015)148
Published for SISSA by Springer
Received: May 11, 2015 Revised: June 5, 2015 Accepted: August 10, 2015 Published: September 22, 2015
Measurement of charm and beauty production at
central rapidity versus charged-particle multiplicity in
proton-proton collisions at
√
s = 7 TeV
The ALICE collaboration
E-mail: [email protected]
Abstract: Prompt D meson and non-prompt J/ψ yields are studied as a function of the multiplicity of charged particles produced in inelastic proton-proton collisions at a centre-of-mass energy of √s = 7 TeV. The results are reported as a ratio between yields in a given multiplicity interval normalised to the multiplicity-integrated ones (relative yields). They are shown as a function of the multiplicity of charged particles normalised to the average value for inelastic collisions (relative charged-particle multiplicity). D0, D+ and D∗+ mesons are measured in five pT intervals from 1 GeV/c to 20 GeV/c and for |y| < 0.5
via their hadronic decays. The D-meson relative yield is found to increase with increasing charged-particle multiplicity. For events with multiplicity six times higher than the average multiplicity of inelastic collisions, a yield enhancement of a factor about 15 relative to the multiplicity-integrated yield in inelastic collisions is observed. The yield enhancement is independent of transverse momentum within the uncertainties of the measurement. The D0-meson relative yield is also measured as a function of the relative multiplicity at forward pseudo-rapidity. The non-prompt J/ψ, i.e. the B hadron, contribution to the inclusive J/ψ production is measured in the di-electron decay channel at central rapidity. It is evaluated for pT> 1.3 GeV/c and |y| < 0.9, and extrapolated to pT> 0. The fraction of non-prompt
J/ψ in the inclusive J/ψ yields shows no dependence on the charged-particle multiplicity at central rapidity. Charm and beauty hadron relative yields exhibit a similar increase with increasing charged-particle multiplicity. The measurements are compared to PYTHIA 8, EPOS 3 and percolation calculations.
Keywords: Hadron-Hadron Scattering ArXiv ePrint: 1505.00664
JHEP09(2015)148
Contents
1 Introduction 1
2 Experimental apparatus and data sample 4
3 Multiplicity definition and corrections 6
4 D-meson analysis 7
4.1 D-meson reconstruction 7
4.2 Corrections 9
4.3 Systematic uncertainties 11
4.4 Results 12
4.4.1 Studies with the charged-particle multiplicity at forward rapidity 13
5 Non-prompt J/ψ analysis 16
5.1 Non-prompt J/ψ reconstruction 16
5.2 Corrections 18
5.3 Systematic uncertainties 19
5.4 Results 21
6 Comparison of charm and beauty production 21
7 Comparison to theoretical calculations 24
7.1 PYTHIA 8 simulations 24
7.2 Comparison of data with models 26
8 Summary 29
A Tables of the results 31
The ALICE collaboration 39
1 Introduction
The study of the production of hadrons containing heavy quarks, i.e. charm and beauty, in proton-proton (pp) collisions at the Large Hadron Collider (LHC) provides a way to test calculations based on perturbative Quantum Chromodynamics (pQCD) at the high-est available collision energies. The inclusive production cross sections of charm mesons measured in pp collisions at the LHC at both central [1, 2] and forward [3] rapidity are described by theoretical predictions based on pQCD calculations with the collinear factori-sation approach at next-to-leading order (e.g. in the general-mass variable-flavour-number
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scheme, GM-VFNS [4]) or at fixed order with next-to-leading-log resummation (FONLL [5–8]) within theoretical uncertainties. The comparisons suggest that charm production is under (over) estimated by the central values of the FONLL (GM-VFNS) calculations. The measured D-meson production cross sections in pp collisions at the LHC can also be described by pQCD calculations performed in the framework of kT-factorisation in the
leading order (LO) approximation [9]. Beauty production cross section measurements in pp collisions at √s = 7 TeV [10–14] are well described by implementations of FONLL and GM-VFNS [7,15]. In the case of B mesons, the measured cross sections are close to the central value of the FONLL and GM-VFNS predictions. A similar situation was observed in pp collisions at √s = 1.96 TeV at the FNAL Tevatron collider [16–18].
The measurement of heavy-flavour production in pp collisions as a function of the charged-particle multiplicity produced in the collision could provide insight into the pro-cesses occurring in the collision at the partonic level and the interplay between the hard and soft mechanisms in particle production. These aspects are expected to depend on the energy and on the impact parameter (the distance between the colliding protons in the plane perpendicular to the beam direction) of the pp collision [19–21]. In the im-pact parameter representation of proton-proton collisions, the overlap of the nucleon wave functions in proton-proton collisions can be described by a geometrical picture with two separate transverse distance scales: the impact parameter of the collision and the transverse spatial partonic distribution [20, 22–24]. In particular, pp collisions with a hard parton-parton scattering are predicted to be more central (i.e. have smaller impact parameter) than minimum-bias events [20,25].
The NA27 Collaboration observed in 1988 that the average charged-particle multiplic-ity in events with open charm production was higher by about 20% than in events without charm production [26]. A softening of the momentum spectra of hadrons produced in as-sociation with charm was also observed. This result was interpreted as a consequence of the more central nature of collisions leading to charm production.
At LHC energies, two additional contributions to charm production and its relation to multiplicity have to be considered. The first effect is the likely larger amount of gluon radiation associated to the short distance production processes at larger energies and par-ticle transverse momenta. The second is the contribution of Multiple-Parton Interactions (MPI) [27–29], i.e. several hard partonic interactions occurring in a single pp collision. In this context, pQCD-inspired models describe the final-state particles produced in hadronic collisions with a two-component approach, namely an initial hard partonic scattering pro-cess, that gives rise to collimated clusters of hadrons (jets), and an underlying event, consisting of the final-state particles that are not associated with the initial hard scat-tering. While the hard scattering process can be computed with a pQCD approach, the description of the underlying event, which is thought to be dominated by particles produced in soft processes and by perturbative (mini)jets with relatively small transverse momenta (soft MPIs), is based on a phenomenological model. In particular, pQCD-based models of MPIs provide a consistent way to describe high multiplicity pp collisions, and have been implemented in recent Monte Carlo generators like PYTHIA 6 [30], PYTHIA 8 [31], and HERWIG [32]. Measurements by the CMS Collaboration of jet and underlying event
prop-JHEP09(2015)148
erties as a function of multiplicity in pp collisions at √s = 7 TeV can be better describedby event generators including MPI [33,34]. The analysis of minijet production performed by the ALICE Collaboration [35] indicates that high multiplicities in pp collisions are reached through a high number of MPIs and a higher than average number of fragments per parton. Upward fluctuations of the gluon density in the colliding protons are also ad-vocated to describe the results from high multiplicity pp collisions at the LHC [21,36,37]. Indeed, the transverse structure of the proton, as probed in hard partonic scattering pro-cesses, is predicted to play a crucial role in defining the underlying event structure and the probability of MPIs [25]. In the heavy-flavour sector, the LHCb Collaboration reported measurements of double charm production in pp collisions at the LHC (D0+ X, J/ψ + X and J/ψ + J/ψ where X = D0, D+, D+s , Λ+c), which suggest that MPIs also play a role at the hard momentum scale relevant for cc production [38,39].
The ALICE Collaboration published the first measurement of inclusive J/ψ production as a function of charged-particle multiplicity, expressed as the pseudo-rapidity density of charged particles dNch/dη at mid-rapidity, in pp collisions at
√
s = 7 TeV [40]. An approximately linear increase of the yield of J/ψ with the charged-particle multiplicity was observed in a multiplicity range reaching four times the average multiplicity hdNch/dηi.
The measurements at |y| < 0.9 and 2.5 < y < 4.0 were compatible within the uncertainties. Both the larger amount of gluon radiation and the contribution of MPI in collisions where heavy quarks are produced can induce a correlation between the yield of quarkonia and the charged-particle multiplicity produced in the collision. The measured rise of J/ψ yield with increasing multiplicity can also be described in the framework of string interaction or parton saturation models. In particular, in ref. [41] a stronger-than-linear trend in the high density domain is anticipated as a consequence of the interaction (overlap) of strings, which reduces the effective number of sources for soft-particle production. The increasing trend of J/ψ yield with multiplicity is also described in a framework in which high multiplicities are attained in pp collisions due to the contribution of higher Fock states in the proton, leading to a larger number of gluons participating in the collision [37].
It is also worth pointing out that the charged-particle densities attained in high-multiplicity pp collisions at the LHC are of the same order of magnitude as those measured in semi-peripheral heavy-ion collisions at lower centre-of-mass energies [42]. In those heavy-ion collisheavy-ions, the measured momentum distributheavy-ions of light hadrons indicate that the sys-tem undergoes a collective expansion, which can be described in terms of hydrodynamics. Recent measurements in high-multiplicity p–Pb collisions at√sNN = 5.02 TeV [43–48] and
in high-multiplicity pp collisions at the LHC [49] indicate that such a collective behaviour could also be at play in these systems. If charm quarks were to follow a collective motion in high-multiplicity events, their momentum spectra would be altered, and the heavy-flavour hadron relative yields at high multiplicity would vary as a function of pT [50].
The measurements of the pT-differential prompt D meson and non-prompt J/ψ cross
sections in pp collisions at √s = 7 TeV with the ALICE experiment at the LHC were published in references [1, 10]. In this paper, we report the measurement of the relative open heavy-flavour production yields as a function of the charged-particle multiplicity in pp collisions at √s = 7 TeV. Open charm and beauty production is measured by
recon-JHEP09(2015)148
structing prompt D mesons and non-prompt J/ψ, i.e. J/ψ mesons coming from the decayof beauty hadrons. The experimental setup and the multiplicity estimation are described in sections 2 and 3, respectively. Prompt D0, D+, D∗+ mesons were measured at central rapidity, |y| < 0.5, in six multiplicity intervals and five pT intervals from 1 GeV/c to 20
GeV/c (section4). The non-prompt fraction of J/ψ production was measured in the rapid-ity interval |y| < 0.9 in five multiplicrapid-ity intervals and for pT > 1.3 GeV/c and extrapolated
to pT > 0 (section5). The relative yields as a function of charged-particle multiplicity are
compared in section 6. Finally, model calculations are discussed and compared with data in section 7.
2 Experimental apparatus and data sample
The ALICE apparatus [51] consists of a central barrel detector covering the pseudo-rapidity interval |η| < 0.9, a forward muon spectrometer covering the pseudo-rapidity interval −4.0 < η < −2.5, and a set of detectors at forward and backward rapidities used for triggering and event characterization. In the following, the subsystems that are relevant for the D meson and non-prompt J/ψ analyses are described.
The central barrel detectors are located inside a large solenoidal magnet, which provides a magnetic field of 0.5 T along the beam direction (z axis in the ALICE reference frame). Tracking and particle identification are performed using the information provided by the Inner Tracking System (ITS), the Time Projection Chamber (TPC) and the Time Of Flight (TOF) detectors, that have full azimuthal coverage in the pseudo-rapidity interval |η| < 0.9. The detector closest to the beam axis is the ITS, which is composed of six cylindrical layers of silicon detectors, with radial distances from the beam axis ranging from 3.9 cm to 43.0 cm. The two innermost layers, with average radii of 3.9 cm and 7.6 cm, are equipped with Silicon Pixel Detectors (SPD). The two SPD layers, covering the pseudo-rapidity ranges of |η| < 2.0 and |η| < 1.4 respectively, have 1200 SPD readout chips. The two intermediate layers are made of Silicon Drift Detectors (SDD), while Silicon Strip Detectors (SSD) equip the two outermost layers. The high spatial resolution of the silicon sensors, together with the low material budget (on average 7.7% of a radiation length for tracks crossing the ITS perpendicularly to the detector surfaces, i.e. η = 0) and the small distance of the innermost layer from the beam vacuum tube, allow for the measurement of the track impact parameter in the transverse plane (d0), i.e. the distance
of closest approach of the track to the primary vertex in the plane transverse to the beam direction, with a resolution better than 75 µm for transverse momenta pT> 1 GeV/c [52].
The SPD provides also a measurement of the multiplicity of charged particles produced in the collision based on track segments (tracklets) built by associating pairs of hits in the two SPD layers.
At larger radii (85 < r < 247 cm), a 510 cm long cylindrical TPC [53] provides track reconstruction with up to 159 three-dimensional space points per track, as well as particle identification via the measurement of the specific energy deposit dE/dx in the gas. The charged particle identification capability of the TPC is supplemented by the TOF [54], which is equipped with Multi-gap Resistive Plate Chambers (MRPCs) located
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at radial distances between 377 and 399 cm from the beam axis. The overall TOF resolutionincluding the uncertainty on the time at which the collision took place, and the tracking and momentum resolution was about 160 ps for the data-taking period considered in these analyses.
The V0 detector [55], used for triggering and for estimating the multiplicity of charged particles in the forward rapidity region, consists of two arrays of 32 scintillators each, placed around the beam vacuum tube on either side of the interaction region at z = −90 cm and z = +340 cm. The two arrays cover the pseudo-rapidity intervals −3.7 < η < −1.7 and 2.8 < η < 5.1, respectively.
The data from proton-proton (pp) collisions at a centre-of-mass energy of √s = 7 TeV used for the analyses were recorded in 2010. The data sample consists of about 314 million minimum-bias (MB) events, corresponding to an integrated luminosity of Lint ' 5 nb−1.
Minimum-bias collisions were triggered by requiring at least one hit in either of the V0 counters or in the SPD (|η| < 2), in coincidence with the arrival time of proton bunches from both directions. This trigger was estimated to be sensitive to about 85% of the inelastic cross section [56].
To enrich the data sample with high multiplicity events, a High Multiplicity (HM) trigger based on the multiplicity information provided by the outer SPD layer was also used. Each readout chip of the SPD promptly asserts a digital pulse, called FastOR bit, on the presence of at least one firing pixel. A sample of about 6 million events was collected applying a selection on the minimum number of readout chips having asserted this digital pulse. The threshold was configured to select the ≈ 0.7% of the events with highest number of hits in the outer SPD layer. This HM-trigger sample (Lint' 14 nb−1) provides
an increase of statistics by a factor of about 2.8 relative to the MB trigger for events with more than 50 tracklets, corresponding to about six times the average multiplicity.
Only events with interaction vertex reconstructed from tracks with a coordinate |z| < 10 cm along the beam line were used for the analysis. In the considered data samples, the instantaneous luminosity was limited to 0.6–1.2 × 1029 cm−2s−1 by displacing the beams in the transverse plane by 3.8 times the RMS of their transverse profile. In this way, the interaction probability per bunch crossing was kept in the range 0.04–0.08, with a probability of collision pile-up below 4% per triggered event. An algorithm to detect multiple interaction vertices based on SPD track segments, or tracklets, was used to further reduce the pile-up contribution. An event is rejected from the analysed data sample if a second interaction vertex is found, which has at least three associated tracklets, and is separated from the first one by more than 0.8 cm along z. This removes about 48% of the pile-up events. The remaining pile-up contamination has two contributions: events with pile-up of collisions with ∆z < 0.8 cm and events in which the piled-up collisions have low-multiplicity (less than three charged particles reconstructed in the SPD). In the case of pile-up of collisions with small separation along z, the multiplicity estimation may be biased because some of the tracklets of charged particles from different interactions may be added together. According to simulations, the number of tracklets results to be biased when the piled-up vertices are separated along z by less than 0.6 cm. Combining this result with the shape of the luminous region along the beam direction and the maximum
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pile-up rate of 4%, the overall probability that two piled-up events induce a bias in thedetermination of multiplicity was found to be lower than 0.3%. The fraction of events with biased number of tracklets increases with increasing multiplicity and it was estimated to be below 2% at the highest multiplicities considered in this analysis, while the resulting bias on the measured number of tracklets was found to be negligible in all the multiplicity classes.
3 Multiplicity definition and corrections
In the present analysis, the experimental estimator of the charged-particle multiplicity is the number of tracklets in the interval |η| < 1.0 (Ntracklets). Tracklets are track segments defined
by combining the clusters in the SPD detector with the reconstructed primary vertex position. Tracklets are required to point to the primary interaction vertex within ±1 cm in the transverse plane and ±3 cm in the z direction [51,52]. This multiplicity estimator is the same as was used in previous studies performed for inclusive J/ψ production [40]. Monte Carlo simulations of the detector response have shown that Ntracklets is proportional to the
pseudo-rapidity density of the generated charged primary particles, dNch/dη, within 2%.
Primary particles are defined as prompt particles produced in the collision and all decay products, except products from weak decays of strange particles. The pseudo-rapidity coverage of the SPD detector changes with the position of the interaction vertex along the beam line, zvtx, and with time due to the variation of the number of inactive channels. The
detector response over the analysed data taking period is equalised by means of a data-based correction, which is applied on an event-by-event basis depending on zvtx and time.
The measurements in the Ntracklets ∈ [1,49] interval are performed using
minimum-bias triggered data, while those in the [50,80] range exploit the SPD-based HM trigger described above. The HM trigger is fully efficient for events with Ntracklets > 65. The
number of events and the D-meson candidate invariant mass distributions were corrected for the HM trigger inefficiency in the Ntracklets ∈ [50,65] range by means of a data-driven
re-weighting procedure. The Ntracklets-dependent event weights were defined from the ratio
of the measured distributions of the number of tracklets in the HM and minimum-bias trigger samples. The effect of this correction on the per-event raw yield was of about 2.5%. The average dNch/dη of events in the highest Ntracklets interval was determined from the
minimum-bias sample.
The analysis results are presented as a function of the relative charged-particle multi-plicity at central rapidity, (dNch/dη)jhdNch/dηi, where hdNch/dηi = 6.01±0.01(stat.)+0.20−0.12
(syst.) is measured in inelastic pp collisions at √s = 7 TeV with at least one charged par-ticle in |η| < 1.0 [57]. The relative quantities are used to minimise the experimental uncertainties and to facilitate the comparison with other measurements and models. The considered Ntracklets intervals and the corresponding relative charged-particle multiplicity
ranges are summarised in table 1. The highest Ntracklets interval considered in the analysis
extends to a multiplicity of about 9 times the hdNch/dηi of inelastic pp collisions and the
average multiplicity of events in this Ntracklets interval is about six times the hdNch/dηi.
deter-JHEP09(2015)148
Ntracklets (dNch/dη)j (dNch/dη)jhdNch/dηi ND 0 events/106 N J/ψ events/106 [1, 8] 2.7 0.45+0.03−0.03 155.1 — [4, 8] 3.8 0.63+0.04−0.04 — 89.0 [9, 13] 7.1 1.18+0.07−0.07 46.2 50.5 [14, 19] 10.7 1.78+0.10−0.11 32.0 35.5 [20, 30] 15.8 2.63+0.15−0.17 24.7 28.0 [31, 49] 24.1 4.01+0.23−0.25 7.9 9.5 [50, 80] 36.7 6.11+0.35−0.39 1.7 —Table 1. Summary of the multiplicity intervals used for the analyses. The number of reconstructed
tracklets Ntracklets, the average charged-particle multiplicity (dNch/dη)j, and the relative
charged-particle multiplicity (dNch/dη)jhdNch/dηi are detailed. The number of events analysed in the
various multiplicity ranges for both the D-meson and J/ψ analyses are reported. The number of
events for the Ntracklets interval [50, 80] are corrected for the high multiplicity trigger efficiency, as
explained in section3.
mination of the Ntracklets to dNch/dη proportionality factor, 2%, (ii) its possible deviation
from linearity, 5%, (iii) and the uncertainty on the measured hdNch/dηi.
The analysis of D0 production is also carried out as a function of the charged-particle multiplicity in the regions −3.7 < η < −1.7 and 2.8 < η < 5.1, as measured with the charge collected by the V0 scintillator counters, NV0, reported in units of the
minimum-ionizing-particle charge. The motivation for studying the multiplicity dependence of charmed-meson production also with this estimator is that the event multiplicity and the D-meson yields are evaluated in different pseudorapidity ranges, reducing the effects of auto-correlations. In contrast, with the Ntracklets estimator also the D-meson decay products and the charged
particles produced in the fragmentation of the same charm quark are included in the multiplicity evaluation. Monte Carlo simulations demonstrate that NV0 is proportional to
the charged-particle multiplicity in that pseudo-rapidity interval. In this paper we report D0 relative yields as a function of the relative uncorrected multiplicity in the V0 detector,
NV0hNV0i (see section 4.4.1).
4 D-meson analysis
4.1 D-meson reconstruction
Charm production was studied by reconstructing D0, D+ and D∗+ mesons, and their an-tiparticles, via their hadronic decay channels D0 → K−π+ (with branching ratio, BR, of
3.88±0.05%), D+→ K−π+π+(BR of 9.13±0.19%), and D∗+ → D0π+(BR of 67.7±0.05%)
with D0 → K−π+ [58]. D-meson candidates were selected with the same strategy as de-scribed in [1]. The selection of D0 and D+ decays (weak decays with mean proper decay
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length cτ ≈ 123 and 312 µm, respectively [58]) was based on the reconstruction ofsec-ondary vertices separated by few hundred microns from the interaction point. In the case of the D∗+ strong decay, the decay topology of the produced D0 was reconstructed. D0 and D+ candidates were formed using pairs and triplets of tracks with the proper charge
sign combination, |η| < 0.8, pT > 0.3 GeV/c, at least 70 associated space points (out of
a maximum of 159) with χ2/ndf < 2 of the momentum fit in the TPC, and at least two hits (out of 6) in the ITS, of which at least one had to be in either of the two SPD layers. D∗+candidates were formed by combining D0 candidates with tracks with pT> 80 MeV/c
and at least 3 hits in the ITS, out of which at least one should be in the SPD. The selec-tion of tracks with |η| < 0.8 limits the D-meson acceptance in rapidity. The acceptance drops steeply to zero for |y| > 0.5 at low pT and |y| > 0.8 at pT > 5 GeV/c. A pT
-dependent fiducial acceptance cut, |yD| < yfid(pT), was therefore applied on the D-meson
rapidity. The cut value, yfid(pT), increases from 0.5 to 0.8 in the transverse momentum
range 0 < pT < 5 GeV/c according to a second-order polynomial function and it takes a
constant value of 0.8 for pT> 5 GeV/c. The selection of the decay topology was based on
the displacement of the decay tracks from the interaction vertex, the separation between the secondary and primary vertices, and the pointing angle of the reconstructed D-meson momentum and its flight line from the primary to the secondary vertex. The selections were tuned such that a large statistical significance of the signal and a selection efficiency as high as possible were achieved, which resulted in cut values that depend on the D-meson pT and species [1]. The same selections were used in all the multiplicity intervals in order
to minimise the effect of efficiency corrections in the ratio of the yields. Pion and kaon identification based on the TPC and TOF detectors were used to obtain a further reduction of the background. Cuts in units of resolution (at ±3 σ) were applied around the expected mean values of energy deposit dE/dx and time-of-flight. Tracks without TOF signal were identified using only the TPC information. Tracks with incompatible TPC and TOF re-sponse were considered as non-identified and were used in the analysis as both pion and kaon candidates. Particle identification (PID) was not applied to the pion tracks from the D∗+ decay. This selection guarantees a reduction of the background by a factor of about 2 to 3 at low pT, while preserving about 95% of the signal.
The D-meson raw yields were extracted in each Ntracklets and pT interval by means of a
fit to the candidate invariant mass distributions (mass difference ∆M = M (Kππ) − M (Kπ) for D∗+). Similarly, the multiplicity-integrated raw yields were also evaluated for each pT
interval. The D0 and D+candidate invariant mass distributions were fitted with a function composed of a Gaussian for the signal and an exponential term that describes the back-ground shape. The ∆M distribution of D∗+ candidates, which features a narrow peak at ∆M ' 145.4 MeV/c2[58], was fitted with a Gaussian function for the signal and a threshold function multiplied by an exponential to model the background √∆M − Mπ· eb(∆M −Mπ).
The centroids of the Gaussians were found to be compatible with the world-average masses of the D mesons [58] in all multiplicity and pT intervals. The widths of the Gaussian
functions are independent of multiplicity and increase with increasing D-meson pT,
rang-ing between 10 and 20 MeV/c2 for D0 and D+ and between 600 and 900 keV/c2 for D∗+ mesons, consistent with the values obtained in simulations. In order to reduce the
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influence of statistical fluctuations, the raw yields were determined by constraining theD-meson line shape, its mass to the world-average D-meson mass, and its width to the value obtained from a fit to the invariant mass distribution in the multiplicity-integrated sample, where the signal statistical significance is larger. Figure 1 shows the D0 and D+
candidate invariant mass distribution, and D∗+ mass difference distributions, for selected pT and multiplicity intervals. The extraction of the raw signal yields (sum of particle and
antiparticle) was possible in five pT intervals from 1 GeV/c to 20 GeV/c for the Ntracklets
ranges reported in table1. The analysis covering the range Ntracklets ∈ [1, 49] exploited the
minimum-bias triggered sample and was possible for the three D-meson species in three pT
intervals in the range between 2 and 12 GeV/c. In addition, the D0 signal was extracted
in Ntracklets ∈ [1, 49] for 1 < pT < 2 GeV/c, and the D∗+ signal was determined in three
multiplicity intervals for 12 < pT< 20 GeV/c. The highest multiplicity interval [50, 80] was
studied with the high multiplicity triggered sample via D0 mesons for 2 < pT < 4 GeV/c
and the three D-meson species for 4 < pT < 8 GeV/c. The raw yield extraction in the
remaining pTand multiplicity intervals for the different D-meson species was not performed
due to the limited statistics in the analysed data sample and/or the large background. 4.2 Corrections
The yields of D mesons were evaluated for each multiplicity and pT interval starting from
the raw counts, Nraw, which were divided by the reconstruction, topological and PID
selec-tion efficiencies for prompt D mesons, εprompt D, and by the number of events analysed in
the considered multiplicity interval, Neventj . The results are reported as the ratio of yields in each multiplicity interval, (d2ND0/dydpT)j, to the multiplicity-integrated (average) yield,
hd2ND0 /dydpTi, d2ND0/dydpT hd2ND0 /dydpTi !j = 1 Neventj Nraw Dj 0 εjprompt D0 ! , 1 NMB trigger εtrigger hNraw D0i hεprompt D0i , (4.1) where the index j identifies the multiplicity interval. The acceptance correction, defined as the fraction of D mesons within a given rapidity and pT interval whose decay particles
are within the detector coverage, cancels in this ratio. D-meson raw yields have two components: the prompt D-meson contribution, and the feed-down contribution originating from B hadron decays. Equation (4.1) evaluates the yields of prompt D mesons under the assumption that the relative contribution to the D-meson raw yield due to the feed-down from B hadron decays does not depend on the multiplicity of the event, and is therefore cancelling in the ratio to the multiplicity-integrated values. This assumption is justified by the measurement of the multiplicity dependence of the B-hadron yields, via the non-prompt J/ψ fraction, presented in section 5 and by PYTHIA simulations. To evaluate the yields per inelastic collisions, the number of events used for the normalisation of the multiplicity-integrated yield has to be corrected for the fraction of inelastic collisions that are not selected by the minimum-bias trigger NMB trigger/εtrigger, with εtrigger= 0.85+6%−3%[56]. The
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) 2 c ) (GeV/ π M(K 1.7 1.8 1.9 2 2.1 ) 2 c Counts/(8 MeV/ 50 100 150 , [1,8] tracklets c <4 GeV/ T p 2< = 7 TeV s pp, -1 = 5 nb int L ALICE 18 ± ) = 154 σ S (3 ) = 0.61 σ S/B (3 ) 2 c ) (GeV/ π M(K 1.7 1.8 1.9 2 2.1 ) 2 c Counts/(8 MeV/ 100 200 300 400 2<pT<4 GeV/c, [14,19] tracklets 38 ± ) = 498 σ S (3 ) = 0.37 σ S/B (3 ) 2 c ) (GeV/ π M(K 1.7 1.8 1.9 2 2.1 ) 2 c Counts/(8 MeV/ 200 400 600 800 2<pT<4 GeV/c, [31,49] tracklets 47 ± ) = 478 σ S (3 ) = 0.19 σ S/B (3and charge conj. + π K → 0 D ) 2 c ) (GeV/ π M(KK 1.7 1.8 1.9 2 ) 2 c Counts/(8 MeV/ 10 20 30 40 4<pT<8 GeV/c, [1,8] tracklets 9 ± ) = 74 σ S (3 ) = 2.69 σ S/B (3 ) 2 c ) (GeV/ π M(KK 1.7 1.8 1.9 2 ) 2 c Counts/(8 MeV/ 20 40 60 80 100 120 140 , [14,19] tracklets c <8 GeV/ T p 4< 19 ± ) = 231 σ S (3 ) = 1.13 σ S/B (3 ) 2 c ) (GeV/ π M(KK 1.7 1.8 1.9 2 ) 2 c Counts/(8 MeV/ 50 100 150 200 , [31,49] tracklets c <8 GeV/ T p 4< 25 ± ) = 269 σ S (3 ) = 0.55 σ S/B (3
and charge conj. + π + π K → + D fhistoInvMass__7__7__16__7__7__7__7__7__7__7__7__7__7__7__7__7__7__7__7__25__7__7__7__7__7__7__7__7__7__7 Entries 100 Mean 0.1475 RMS 0.003413 ) 2 c ) (GeV/ π )-M(K π π M(K 0.14 0.145 0.15 0.155 ) 2 c Counts/(1 MeV/ 5 10 15 20 25 30 fhistoInvMass__7 Entries 100 Mean 0.1475 RMS c, [1,8] tracklets 0.003413 <12 GeV/ T p 8< 5 ± ) = 25 σ S (3 ) = 2.42 σ S/B (3 ) 2 c ) (GeV/ π )-M(K π π M(K 0.14 0.145 0.15 0.155 ) 2 c Counts/(0.5 MeV/ 10 20 30 40 50 60 , [14,19] tracklets c <12 GeV/ T p 8< 10 ± ) = 106 σ S (3 ) = 3.12 σ S/B (3 ) 2 c ) (GeV/ π )-M(K π π M(K 0.14 0.145 0.15 0.155 ) 2 c Counts/(0.5 MeV/ 10 20 30 40 50 60 8<pT<12 GeV/c, [31,49] tracklets 14 ± ) = 91 σ S (3 ) = 0.73 σ S/B (3
and charge conj. + π 0 D → *+ D
Figure 1. D0 and D+ invariant mass and D∗+ mass difference distributions for selected p
T and
Ntracklets intervals for pp collisions at
√
s = 7 TeV with Lint = 5 nb−1. The D0 distributions are
shown for 2 < pT< 4 GeV/c (top-panels), the D+ for 4 < pT< 8 GeV/c (middle-panels), and the
D∗+ for 8 < p
T < 12 GeV/c (bottom-panels). The Ntracklets ∈ [1,8], [14,19] and [31,49] intervals
are shown in the left, middle and right panels respectively. The fits to the candidate invariant mass distributions are also shown.
verified with PYTHIA 6.4.21 [30] Monte Carlo simulations that this minimum-bias trigger is 100% efficient for D mesons in the kinematic range of this measurement.
The D-meson efficiency corrections were determined with Monte Carlo simulations us-ing the PYTHIA 6.4.21 event generator [30] with Perugia-0 tune [59], and the GEANT3 transport code [60]. The detector configuration and the LHC beam conditions were in-cluded, taking into account their evolution with time during the data taking period. The
εjprompt Ddepends on the D-meson species and on pT. For prompt D0 mesons it is 3–4% in
the 2 < pT < 4 GeV/c interval and it increases up to 25–35% for pT > 8 GeV/c, because
less stringent topological selections were used at high pT, where the combinatorial
back-ground is smaller. The efficiency for feed-down D mesons is larger by about 20–30% than for prompt D mesons. This is due to the fact that feed-down D mesons decay further away from the interaction vertex and are therefore more efficiently selected by the topological requirements. The D-meson selection efficiency depends also on the multiplicity of charged particles produced in the collision, because the resolution on the position of primary vertex
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improves with increasing multiplicity, providing a better resolution of the variables usedfor the topological selections. For example, the D0 selection efficiency in 2 < pT< 4 GeV/c
increases by about 40% from the lowest to the highest multiplicity intervals considered in this analysis.
4.3 Systematic uncertainties
Several sources of systematic uncertainty that could affect the relative yields as expressed in eq. (4.1) were studied. Only the raw yield extraction and the feed-down subtraction contribution were found to have an influence on the relative yields. The influence of the raw signal extraction from the invariant mass distribution was evaluated by using the raw yields obtained with different approaches to separate the signal from the combinatorial background. The contribution to the D0 line shape of mis-identified K and π pairs from D0 decays, e.g. a D0 → K−π+ that passes the selection criteria as D0 → π−K+, was
assumed to be the same in all multiplicity intervals and was neglected in this analysis. Different background fit functions were considered (exponential, polynomial, linear for D0 and D+; threshold, (∆M − Mπ)b, for D∗+); the centroid and width of the Gaussians were
left as free parameters in the fit instead of keeping them fixed to the values obtained from the multiplicity-integrated distribution; the raw yield was also extracted by counting the invariant mass histogram entries in a ±3σ interval around the peak after subtracting the background evaluated by fitting the distribution side bands (i.e. excluding the ±3σ interval around the centroid). The uncertainty was estimated from the stability of the ratio of the raw yields Nraw Dj 0/hNraw D0i, where the same raw yield extraction method was used in the multiplicity interval j and for the multiplicity-integrated result. The assigned systematic uncertainty varies from 3% to 15% depending on the meson species, pT and multiplicity
interval.
The efficiency corrections were calculated independently for each multiplicity interval. The multiplicity distribution of primary charged particles in the Monte Carlo simulation, P (Nch), was tuned to reproduce the measured charged-particle multiplicity [57]. The
effi-ciencies obtained with different Monte Carlo setups, that generate different initial multi-plicity distributions, showed a good agreement in all multimulti-plicity intervals. This effect was not considered as a source of systematic uncertainty.
The D-meson decay tracks can be included or not in (i) the counting of the number of tracklets, resulting in a shift of the estimated multiplicity, and in (ii) the determina-tion of the primary vertex posidetermina-tion, which leads to a different resoludetermina-tion on the vertex position and of the geometrical variables used for the D-meson selection. In the default configuration, the analysis was done excluding the D-meson decay tracks from the primary vertex determination and without excluding them from the multiplicity estimation. To check for possible systematic effects due to the multiplicity determination, the analysis was repeated excluding the D-meson decay tracks from the multiplicity estimation, obtaining compatible results. Furthermore, the relative yields were determined without excluding the D-meson decay tracks from the primary vertex determination. The influence of such variation is properly reproduced by Monte Carlo simulations, leading to a null effect on the
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corrected relative yields. Therefore this effect was not considered as a source of systematicuncertainty.
The analysis was repeated for all D-meson species with different sets of topological selection criteria. It was verified that the corrected relative D-meson yields as defined in eq. (4.1) are not sensitive to this variation. This confirmed that the systematic uncertainty related to the topological selection description in the Monte Carlo cancels in the ratio. The influence of the PID strategy, which is based on the information of TPC and TOF detectors, was studied by also extracting the D-meson raw yields without PID selection criteria, which could be done only for D-meson pT> 2 GeV/c. The ratios of the relative raw
yields, Nraw Dj 0/hNraw D0i, with and without PID selections were found to be compatible with unity. As a consequence, this effect was not considered as a source of systematic uncertainty.
As mentioned above, eq. (4.1) describes the prompt corrected yields under the assump-tion that the fracassump-tion of prompt D mesons, fprompt, does not vary with the event
multi-plicity. To estimate the uncertainty related to this assumption, the multiplicity integrated
fprompt factor was evaluated with the FONLL B-hadron production cross sections [7], the
B → D+X decay kinematics from EvtGen [61], and the acceptance, reconstruction and selection efficiency of D mesons from B decays as described in [1]. The resulting fprompt
values are about 85–95% depending on the D-meson pT and the applied selection criteria.
The uncertainty due to the B feed-down contribution to the relative yields, fB= 1−fprompt,
was evaluated assuming a linear increase of the fraction fBj/hfBi from 1/2 to 2 from the
lowest to the highest multiplicity interval. The resulting uncertainties vary with the pT and
multiplicity range and are different for the three mesons. Typical values for intermediate pT at low multiplicity are+5−0%, and at high multiplicity +0−20%.
4.4 Results
The results of the D0, D+ and D∗+ meson relative yields for each pT interval are presented
in figures 2 and 3 as a function of the relative charged-particle multiplicity. The relative yields are presented in the top panels with their statistical (vertical bars) and systematic (boxes) uncertainties except the uncertainty on the feed-down fraction, which is drawn separately in the bottom panels in the form of relative uncertainties. The position of the points on the abscissa is the average value of the relative charged-particle multiplicity, (dNch/dη)hdNch/dηi, for every Ntracklets interval. The D0, D+ and D∗+ meson relative
yields are compatible in all pT intervals within uncertainties.
The average of D0, D+and D∗+ relative yields was computed for each pT interval using
as weights the inverse square of their relative statistical uncertainties. The yield extraction uncertainty was considered as uncorrelated systematic uncertainty. The feed-down fraction systematic uncertainty was treated as a correlated systematic uncertainty. The average of the D-meson relative yields for all pT intervals is summarised in tables 3 and 4, and
presented in figure 4(a). The relative D-meson yields increase with the charged-particle multiplicity by about a factor of 15 in the range between 0.5 and six times hdNch/dηi.
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〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 5 10 15 20 25 c <2 GeV/ T p meson, 1< 0 D ALICE |<0.5 y = 7 TeV, | s pp not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ±+6%/-3% normalization unc. not shown
〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(a) D meson with 1 < pT< 2 GeV/c.
〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 5 10 15 20 25 c <4 GeV/ T p meson, 2< 0 D c <4 GeV/ T p meson, 2< + D c <4 GeV/ T p meson, 2< + D* ALICE |<0.5 y = 7 TeV, | s pp not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ±
+6%/-3% normalization unc. not shown
〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(b) D meson with 2 < pT< 4 GeV/c.
Figure 2. D0, D+ and D∗+ meson relative yields for each p
T interval as a function of
charged-particle multiplicity at central rapidity. The relative yields are presented on the top panels with their statistical (vertical bars) and systematic (boxes) uncertainties, except for the feed-down fraction
uncertainty that is drawn separately in the bottom panels. D0mesons are represented by red circles,
D+ by green squares, and D∗+ by blue triangles. The position of the points on the abscissa is the
average value of (dNch/dη)hdNch/dηi. For D+and D∗+ mesons the points are shifted horizontally
by 1.5% to improve the visibility. The diagonal (dashed) line is also shown to guide the eye.
intervals with respect to the 2 < pT < 4 GeV/c interval values. The yield enhancement is
independent of transverse momentum within the uncertainties of the measurement. 4.4.1 Studies with the charged-particle multiplicity at forward rapidity In the analysis described above, D-meson yields were measured in the same rapidity inter-val as the charged-particle multiplicity. This could lead to a bias if the particles produced in the charm-quark fragmentation and in the D-meson decay would amount to a large fraction of the measured charged particles. In order to study this possible bias, the mea-surement of the D0 yields at central rapidity was also performed as a function of the relative charged-particle multiplicity at forward-rapidity. The charge collected by the V0 scintillator counters, covering −3.7 < η < −1.7 and 2.8 < η < 5.1, was used as multi-plicity estimator in this case. The multimulti-plicity value NV0 was evaluated by dividing the
collected charge by the expected average minimum-ionizing-particle charge. The D0 yields were evaluated in intervals of NV0, and corrected as previously described and summarised
in eq. (4.1). The relative yields of D0 mesons are presented in figure 5 as a function of the relative mean multiplicity measured with the V0 counters, NV0hNV0i. The
statis-tical (systematic) uncertainties are represented by the verstatis-tical bars (empty boxes). The systematic uncertainties due to the raw yield extraction and the B feed-down contribution were determined as explained in section 4.3. The uncertainty due to the unknown
feed-JHEP09(2015)148
〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 5 10 15 20 25 c <8 GeV/ T p meson, 4< 0 D c <8 GeV/ T p meson, 4< + D c <8 GeV/ T p meson, 4< + D* ALICE |<0.5 y = 7 TeV, | s pp not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ±+6%/-3% normalization unc. not shown
〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(a) D meson with 4 < pT< 8 GeV/c.
〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 5 10 15 20 25 c <12 GeV/ T p meson, 8< 0 D c <12 GeV/ T p meson, 8< + D c <12 GeV/ T p meson, 8< + D* ALICE |<0.5 y = 7 TeV, | s pp not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ±
+6%/-3% normalization unc. not shown
〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(b) D meson with 8 < pT< 12 GeV/c.
〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 5 10 15 20 25 c <20 GeV/ T p meson, 12< + D* ALICE |<0.5 y = 7 TeV, | s pp not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ±
+6%/-3% normalization unc. not shown
〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(c) D meson with 12 < pT< 20 GeV/c.
Figure 3. D0, D+ and D∗+ meson relative yields for each p
T interval as a function of
charged-particle multiplicity at central rapidity. The relative yields are presented on the top panels with their statistical (vertical bars) and systematic (boxes) uncertainties, except for the feed-down fraction
uncertainty that is drawn separately in the bottom panels. D0mesons are represented by red circles,
D+ by green squares, and D∗+ by blue triangles. The position of the points on the abscissa is the
average value of (dNch/dη)hdNch/dηi. For D+and D∗+ mesons the points are shifted horizontally
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〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 5 10 15 20 25 c < 2 GeV/ T p 1 < c < 4 GeV/ T p 2 < c < 8 GeV/ T p 4 < c < 12 GeV/ T p 8 < c < 20 GeV/ T p 12 < = 7 TeV s ALICE, pp |<0.5 y meson, | + , D* + ,D 0 Average D not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ±+6%/-3% normalization unc. not shown
〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(a) pTdependence. ) c <4 GeV/ T p ) in 2< T pd y /d N 2 Ratio to (d 0.5 1 1.5 2 2.5 3 3.5 4 c < 2 GeV/ T p 1 < c < 8 GeV/ T p 4 < c < 12 GeV/ T p 8 < c < 20 GeV/ T p 12 < = 7 TeV s ALICE, pp |<0.5 y meson, | + , D* + ,D 0 Average D not shown 〉 η /d N d 〈 ) / η /d N 6% unc. on (d ± 〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 6 7 8 9 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
(b) Ratios of pTintervals vs the 2 < pT< 4 GeV/c.
Figure 4. Average of D0, D+ and D∗+ relative yields as a function of the relative
charged-particle multiplicity at central rapidity. (a) Average of D-meson relative yields in pT intervals.
(b) Ratio of the average relative yields in all pT intervals with respect to that of the 2 < pT <
4 GeV/c interval. The results are presented in the top panels with their statistical (vertical bars) and systematic (boxes) uncertainties, except for the feed-down fraction uncertainty that is drawn separately in the bottom panels. The position of the points on the abscissa is the average value of
(dNch/dη)hdNch/dηi. For some pTintervals the points are shifted horizontally by 1.5% to improve
the visibility. The dashed lines are also shown to guide the eye, a diagonal on (a) and a constant on (b).
down fraction evolution with the charged-particle multiplicity is drawn separately in the bottom panels. The points are located on the x-axis at the average value of the relative mean multiplicity, NV0hNV0i. The uncertainty on the mean multiplicity values, NV0,
was determined by comparing the mean and median values of the distributions. It was found to be below 3% for each multiplicity interval, and about 24% for the multiplicity integrated value. The uncertainty on NV0hNV0i is not displayed on this figure. These
results are also summarised in tables 5and 6. The D0 relative yields increase with the rel-ative uncorrected multiplicity at forward rapidity, as measured with the V0 detector. The results in the 2 < pT < 4 GeV/c and 4 < pT < 8 GeV/c intervals are compatible within
uncertainties. The results with the V0 multiplicity estimator indicate that the increase of the D-meson yield with the event multiplicity observed with the mid-rapidity estimator is not related to the fact that charmed mesons, originating from the fragmentation of charm quarks produced in hard partonic scattering processes, and the charged particle multiplicity are measured in the same pseudo-rapidity range. A qualitatively similar increasing trend of D-meson yield with multiplicity is indeed observed also when an η gap is introduced between the regions where the D-mesons and the multiplicity are measured.
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〉 T pd y /d N 2 d〈 ) / T pd y /d N 2 (d 1 2 3 4 5 6 7 c < 4 GeV/ T p 2 < c < 8 GeV/ T p 4 < = 7 TeV s ALICE, pp |<0.5 y meson, | 0 D not shown 〉 V0 N 〈 / V0 N 3% unc. on ±+6%/-3% normalization unc. not shown
〉 V0 N 〈 / V0 N 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 B feed-down unc. 0.4− 0.2 − 0 0.2
0.4 B fraction hypothesis: × 1/2 (2) at low (high) multiplicity
Figure 5. D0 meson relative yields at |y| < 0.5 for two pT intervals as a function of the relative
charged-particle multiplicity, NV0, measured at −3.7 < η < −1.7 and 2.8 < η < 5.1. The relative
yields are presented on the top panels with their statistical (vertical bars) and systematic (boxes) uncertainties, except the uncertainty on the feed-down fraction which is drawn separately in the
bottom panels. The position of the points on the abscissa is at the average value of NV0hNV0i,
shifted by 1.5% to improve the visibility. The diagonal (dashed) line is also shown to guide the eye.
5 Non-prompt J/ψ analysis
5.1 Non-prompt J/ψ reconstruction
The fraction of non-prompt J/ψ in the inclusive J/ψ yields, fB, was measured as a function
of the charged-particle multiplicity by studying displaced J/ψ mesons that decay into electron pairs in the rapidity range |y| < 0.9. This measurement, combined with the inclusive J/ψ relative yield [40], provides the multiplicity dependence of the production of beauty hadrons. J/ψ candidates were formed by combining pairs of opposite-sign electron tracks. The tracks were required to have pT> 1 GeV/c, at least 70 (out of a maximum of
159) associated space points in the TPC with a χ2/ndf of the momentum fit lower than 2, and to point back to the primary interaction vertex within 1 cm in the transverse plane. The tracks were also required to have at least one associated hit in the SPD detector, with the constraint that one of the two tracks should have a hit in the first SPD layer. Electron identification was based only on the TPC information. A selection of ±3σ around the expected mean values of the specific energy deposit dE/dx for electrons was used. To further reduce the background, a ±3.5σ (±3σ) exclusion band around the expected mean specific energy deposit for pions (protons) was also applied. In order to reduce the combinatorial background, electron candidates compatible, together with a positron candidate, with being products of γ-conversions (invariant mass below 100 MeV/c2) were removed.
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The measurement of fBis based on a statistical discrimination of J/ψ mesons producedat a secondary vertex displaced from the primary pp collision vertex. The signed projection of the J/ψ flight distance onto its transverse momentum vector, ~pT, was constructed as
Lxy =~L · ~pT
/pT, where ~L is the vector from the primary vertex to the J/ψ decay vertex.
The pseudo-proper decay length x = (c · Lxy· m)pT was calculated from the observed
decay length using the world-average J/ψ mass m(J/ψ) = 3096.916 ± 0.011 MeV/c2 [58]. The fraction of non-prompt J/ψ can be determined from a 2-dimensional un-binned log-likelihood fit to x and the unlike-sign di-electron invariant mass distributions. The fit procedure and the functions used to describe the invariant mass and the pseudo-proper decay length distributions were introduced in [10].
The fraction of non-prompt J/ψ as a function of the relative charged-particle multi-plicity was determined for pT > 1.3 GeV/c in five multiplicity intervals in the Ntracklets
range [4, 49]. The Ntracklets ∈ [1, 3] range was excluded from this analysis due to the poor
pseudo-proper decay length resolution, R(x), and the presence of a bias in the determi-nation of x in the case of non-prompt candidates. The resolution of the pseudo-proper decay length is determined with Monte Carlo simulations evaluating the RMS of the x distributions of reconstructed promptly produced J/ψ mesons. The event primary vertex can be computed with or without removing the decay tracks of the J/ψ candidates. The removal of the decay tracks causes a degradation of the resolution on x, especially in the low-multiplicity intervals, as a consequence of the lower precision in the determination of the primary vertex with a reduced number of tracks. For simulated events with non-prompt J/ψ, the removal of the decay tracks also results in a shift of the primary vertex position away from the secondary decay vertex of the beauty hadrons, which is reflected in a sys-tematic shift of the mean of the x distribution. However, one should consider that beauty quarks are always produced in pairs: the two decay tracks from the non-prompt-J/ψ, when included, pull the primary vertex towards the beauty hadron decay vertex, but the charged tracks from the decay of the second beauty quark, which enter in the barrel acceptance, pull the primary vertex in the opposite direction. The shift is larger in the lowest multi-plicity bin where it reaches about 35 µm. This bias is reduced when the J/ψ decay tracks are kept in the evaluation of the primary vertex. The effect of the bias, estimated with Monte Carlo simulations, is a reduction1 of the measured fB by about 20% for events with
Ntracklets = 4, and it becomes negligible for Ntracklets > 10. Therefore, the primary vertex
was computed considering all reconstructed tracks. To correct for the remaining bias, a modification in the resolution function, R(x), used to describe the non-prompt J/ψ in the likelihood fit function was introduced, which depends on Ntracklets. In particular, the shape
of the resolution function was adjusted to obtain a good matching between the function used to describe the non-prompt J/ψ in the likelihood fit (a convolution of a template of the x distribution of J/ψ from beauty hadron decays with the resolution function [10]) and the pseudo-proper decay length distribution of reconstructed secondary J/ψ from Monte Carlo simulations.
1This shift would be greater than 50 µm in the N
tracklets interval [1, 3], leading to a large bias on the extracted fBvalue (up to 35%). The correction for this bias would introduce a large systematic uncertainty.
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2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 ) 2 c Entries/(40 MeV/ 2 4 6 8 10 12 14 16 ALICE, pp s = 7 TeV -1 = 5.6 nb int L c )>1.3 GeV/ ψ (J/ T p |<0.9, y | [4,8] tracklets Data Fit, all Fit, signal Fit, background 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 5 10 15 20 25 [9,13] tracklets 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 5 10 15 20 25 30 [14,19] tracklets 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 5 10 15 20 25 30 35 40 [20,30] tracklets ) 2 c ) (GeV/ -e + M(e 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 5 10 15 20 25 30 35 [31,49] tracklets -2000 -1500 -1000 -500 0 500 1000 1500 2000 m) µ Entries/(40 -1 10 1 10 2 c ) < 4.0 GeV/ -e + (e M 2.4 < Data Fit, all ψ Fit, prompt J/ ψ Fit, non-prompt J/ Fit, background -2000 -1500 -1000 -500 0 500 1000 1500 2000 -1 10 1 10 -2000 -1500 -1000 -500 0 500 1000 1500 2000 -1 10 1 10 -2000 -1500 -1000 -500 0 500 1000 1500 2000 -1 10 1 10 m) µ Pseudo-proper decay length ( -2000 -1500 -1000 -500 0 500 1000 1500 20001 10
Figure 6. J/ψ invariant mass and pseudo-proper decay length distributions in several multiplicity intervals with superimposed the likelihood fit results. The contributions of the signal, the back-ground and their sum are represented with dashed, dot-dashed and full lines, respectively. In addition, the pseudo-proper decay length figures include the prompt and non-prompt contributions to the inclusive yields with dotted and long-dashed lines.
Figure 6presents the invariant mass and pseudo-proper decay length distributions for pT > 1.3 GeV/c for each multiplicity interval together with a projection of the result of
the log-likelihood fit. 5.2 Corrections
For all multiplicity intervals, the measured fraction of non-prompt J/ψ, fB0, was corrected using the acceptance and reconstruction efficiency of prompt, hAcc × εiprompt, and
non-prompt J/ψ, hAcc × εiB, as
fB= 1 +1 − f 0 B fB0 · hAcc × εiB hAcc × εiprompt
−1
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Here all terms refer to non-prompt J/ψ with pT > 1.3 GeV/c. The corrections forac-ceptance and efficiency were computed using Monte Carlo simulations using the GEANT3 transport code [60]. Prompt J/ψ were generated with a pT distribution extrapolated from
CDF measurements [16] and a y distribution parameterised with the Colour Evaporation Model (CEM) [62, 63]. Beauty hadrons were generated using the PYTHIA 6.4.21 event generator [30] with Perugia-0 tune [64]. The acceptance times efficiency values for prompt and non-prompt J/ψ have a minimum of 8% at pT = 2 GeV/c and a broad maximum
of 12% at pT = 7 GeV/c [65]. The relative difference in efficiency between prompt and
non-prompt J/ψ is only about 3%. The ratio hAcc × εiB/hAcc × εiprompt is assumed to be
independent of multiplicity. The uncertainty related to this assumption is discussed in the next section.
The measured non-prompt J/ψ fractions were extrapolated from pT > 1.3 GeV/c down
to pT = 0 using
fBextr(pT> 0) = αextr· fB(pT> 1.3 GeV/c); αextr=
fBmodel(pT> 0)
fmodel
B (pT> 1.3 GeV/c)
, (5.2)
where fBmodel represents a functional form modelled on existing data. It was calculated as the ratio of the differential cross section of non-prompt J/ψ, as obtained with FONLL calculations [7], to that of inclusive J/ψ, parameterised by the phenomenological function defined in [66]: fBmodel(pT) = d2σJ/ψ←hFONLL B dydpT , d2σphenom J/ψ dydpT . (5.3)
A combined fit to the existing results of fB in pp collisions at 7 TeV [10,13,67,68] in the
rapidity bin closest to central rapidity was performed to determine the parameters of the phenomenological parameterisation. The extrapolation factor obtained is αextr = 0.99+0.01−0.03. Its uncertainties were determined by repeating the fit by (i) excluding the LHCb data points at forward rapidities, and (ii) using for the non-prompt J/ψ cross section the upper and lower uncertainty bands of the FONLL predictions, obtained by varying the factorisation and renormalisation scales, instead of the central values. The uncertainties were determined by the maximum and minimum αextr values obtained from these fit variations. The fB
fractions in all multiplicity intervals were extrapolated using the same αextrvalue, evaluated from the fit of the multiplicity integrated measurements.
5.3 Systematic uncertainties
The systematic uncertainty introduced by the experimental resolution on the primary ver-tex position was evaluated by repeating the fitting procedure in two alternative ways: (i) the primary vertex was evaluated without removing the decay tracks of the J/ψ candi-dates. The fit was performed using the standard resolution function for non-prompt J/ψ, that does not depend on multiplicity, but the x distribution of the non-prompt J/ψ was shifted by a multiplicity-dependent value, which was determined by the Monte Carlo sim-ulation. (ii) The event primary vertex was computed after removing the decay tracks of the J/ψ candidates and the fit was performed using the corresponding degraded resolution
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function R(x) and without any shift. The resulting uncertainties decrease withincreas-ing multiplicity, rangincreas-ing from 19% in the lowest multiplicity interval to 3% at the highest multiplicities.
The uncertainty related to the extrapolation of fB from pT > 1.3 GeV/c to pT > 0
was estimated with the method discussed above and it is about 3%. This uncertainty was assumed to be uncorrelated among the multiplicity intervals.
The resolution function used in the fits is based on Monte Carlo simulations, which might introduce systematic effects. These were estimated by repeating the log-likelihood fits modifying the resolution function, R(x), according to (1/(1 + δ)) · R (x/(1 + δ)), where δ is the relative variation of the RMS of the resolution function, and it was varied from −0.1 to +0.1 to take into account the uncertainties in the Monte Carlo description. The systematic uncertainty due to the resolution function increases with multiplicity from 8% to 20%.
The pT distribution of the signal candidates (prompt and non-prompt J/ψ) could
depend on the event multiplicity which could affect the shape of the resolution function which depends on the J/ψ pT. The average pT of the signal candidates was estimated from
data in each multiplicity interval and found to be constant as a function of event multiplicity within statistical uncertainties about ±10%. The influence of a hpTi variation on the
resolution function was determined using Monte Carlo simulations: the pT distribution
was changed, considering softer or harder pT distributions, in order to obtain a ±10%
variation of the hpTi. The corresponding variations obtained for the RMS of the resolution
function are +7% and −8.5% for the softer and harder pT distribution, respectively. The
latter variations are within those quoted for the resolution function (±10%), therefore no additional uncertainty was included.
The acceptance times efficiency values of prompt and non-prompt J/ψ reconstructed for pT > 1.3 GeV/c are of the order of 10% and differ by 3%. The influence of the pT
shape assumed in the simulation on the ratio hAcc × εiB/hAcc × εiprompt was evaluated by
varying the average pT of the simulated J/ψ distributions within ±50%. A 1% variation
in the acceptance was obtained both for prompt and non-prompt J/ψ. The corresponding variation obtained on fB through the eq. (5.1) is about 1%.
The pseudo-proper decay length shape of the combinatorial background was deter-mined by a fit to the x distribution of the candidates in the sidebands of the invariant mass [10]. By varying the fit parameters within their errors an envelope of distributions was obtained, whose extremes were used in the likelihood fit to estimate the systematic uncertainty. It increases slightly with multiplicity, ranging from 1% to 5%.
The uncertainty on the background invariant mass shape, which was determined by fits to the invariant mass distributions of opposite-sign candidates in each multiplicity bin, was evaluated by using like-sign distributions instead, adopting the same procedure as described in [10]. The systematic uncertainty is about 7%, independent of the charged-particle multiplicity.
The shape of the x distribution of J/ψ from b-hadrons was evaluated using PYTHIA 6.4.21 [30]. The systematic uncertainty on its shape was computed by (i) changing the b-hadron decay kinematic, using EvtGen [61] instead of PYTHA 6.4.21 or (ii) by assuming
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a harder and a softer b-hadron pTdistribution, resulting in a hpTi variation of about ±15%.The resulting systematic uncertainty is about 3%, constant with multiplicity.
The signal invariant mass shape was fixed from the Monte Carlo simulation which includes the detector resolution effects and the radiative decays using the EvtGen [61] package. The effect on the invariant mass signal shape due to the uncertainty on the detector material was studied with dedicated Monte Carlo simulations, where the detector material budget was varied by ±6% with respect to the nominal values [69, 70]. The resulting systematic uncertainty on fB is 3% in the lowest event multiplicity interval and
5% in the highest one.
The systematic uncertainties on the pseudo-proper decay length of the combinatorial background, on the pT-extrapolation uncertainty αextr and on the invariant mass shape of
background are found or, in the case of αextr, assumed to be uncorrelated among multi-plicity intervals. The remaining systematic uncertainties are (fully or partially) correlated in different multiplicity intervals.
5.4 Results
The relative yield of J/ψ from beauty hadron decays as a function of the charged-particle multiplicity was evaluated from the inclusive J/ψ yield and the fraction of non-prompt J/ψ per multiplicity interval:
dNJ/ψnon−prompt/dy D dNJ/ψnon−prompt/dyE = dNJ/ψ/dy dNJ/ψ/dy · fB hfBi. (5.4)
fB is the fraction of non-prompt J/ψ in each multiplicity interval, hfBi is the fraction in
the multiplicity integrated sample [10], and (dNJ/ψ/dy)hdNJ/ψ/dyi is the inclusive J/ψ relative yield measured for pT> 0 in each multiplicity interval normalized to its value in
inelastic pp collisions [40]. All these quantities were measured using the same data sam-ple and the statistical correlations were taken into account. In the first charged-particle multiplicity class Ntracklets ∈ [4, 8], which is used for the non-prompt J/ψ analysis
pre-sented here, the relative yield of inclusive J/ψ normalized to the inelastic cross section is (dNJ/ψ/dy)hdNJ/ψ/dyi = 0.41 ± 0.07 (stat) ± 0.01 (syst). The values of fBextrapolated to
pT > 0 were used in eq. (5.4), providing the non-prompt J/ψ relative yields for pT > 0. The
relative yields of inclusive J/ψ were also recomputed for pT > 1.3 GeV/c and no difference
was observed with respect to those for pT > 0 within the uncertainties.
The results for the fraction of non-prompt J/ψ for both pT > 0 and pT> 1.3 GeV/c,
the relative yields of prompt and non-prompt J/ψ in each multiplicity bin for pT > 0 are
summarized in tables 7and 8 and shown in figure 7.
6 Comparison of charm and beauty production
Figure 8(a) presents prompt D meson and inclusive J/ψ results to compare open and hidden charm production. The average prompt D-meson results are shown in the 2 <
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〉 η /d ch N d 〈 ) / η /d ch N (d 0 1 2 3 4 5 from b hadrons (%) ψ Fraction of J/ 0 10 20 30 40 50 = 7 TeV s ALICE, pp c ) > 1.3 GeV/ ψ (J/ T p | < 0.9, y |Figure 7. Non-prompt J/ψ fraction as a function of the relative charged-particle multiplicity at
cen-tral rapidity for pT> 1.3 GeV/c. The vertical bars represent the statistical uncertainties, while the
empty boxes stand for the systematic uncertainties. The width and the height of these empty boxes indicate the measurement uncertainty on the horizontal and vertical axis respectively. The dashed
line shows the value of fBmeasured in the same pTrange and integrated over multiplicity [10]. The
shaded area represents the statistical and systematic uncertainties on the multiplicity-integrated result added in quadrature.
pT < 4 GeV/c interval with the pT-integrated inclusive J/ψ measurement2 at central and
forward-rapidity by the ALICE experiment [40]. The results for prompt J/ψ at central rapidity from this paper (pT > 0) and for prompt D mesons (2 < pT < 4 GeV/c) are
compared in figure 8(b). A similar increase of the relative yield with the charged-particle multiplicity is observed for open and hidden charm production both at central and forward rapidities.
Figure 8(c) superimposes the open charm and beauty production measurements re-ported in this paper showing the average prompt D-meson results in the 2 < pT< 4 GeV/c
interval and the pT-integrated non-prompt J/ψ measurement at central rapidity. The
re-sults are compatible within the measurement uncertainties.
Open charm, open beauty and hidden charm hadron relative yields present a similar in-crease with charged-particle multiplicity. The comparison of open and hidden heavy flavour production suggests that this behaviour is most likely related to the c¯c and b¯b production processes, and is not significantly influenced by hadronisation. The enhancement of the heavy-flavour relative yields with the charged-particle multiplicity is qualitatively consis-tent with the calculations of the contribution from MPIs to particle production at LHC
2
After the inclusive J/ψ measurement was published in reference [40], there was an improvement of the ALICE measurement of the inelastic cross section in pp collisions at√s = 7 TeV. The improved evaluation of the inelastic cross section does not rely on Monte Carlo, hence the systematic uncertainty is larger [56]. To allow a proper comparison with the results reported here, we updated the published inclusive J/ψ measurement by the corresponding change of the trigger efficiency for inelastic collisions 0.864/0.85. The normalisation uncertainties were also changed from 1.5% to+6
